Dynamic responses of flexible-link mechanisms with passive/active damping treatment

This work presents a finite element formulation for non-linear transient dynamic analysis of adaptive beams. The main contribution of this work concerns the development of an original co-rotational sandwich beam element, which allows large displacements and rotations, and takes active/passive damping into account. This element is composed of a viscoelastic core and elastic/piezoelectric laminated faces. The latter are modeled using classical laminate theory, where the electromechanical coupling is considered by modifying the stiffness of the piezoelectric layers. For the core, a four-parameter fractional derivative model is used to characterize its viscoelastic dissipative behavior. Equations of motion are solved using an incremental-iterative method based on the Newmark direct time integration scheme in conjunction with the Grünwald approximation of fractional derivatives, and the Newton–Raphson algorithm.